The first rigorous work that derived precise late-time asymptotics is [1]}, [2]}, [3]}. This work obtained asymptotics for general solutions \(\psi \)  (without any assumptions on the angular frequency) to the wave equation on sub-extremal Reissner–Nordström spacetimes. Precise asymptotics were obtained in [4]} for some general asymptotically flat spacetimes that include as a special case the subextremal Kerr family of black hole spacetimes, and in [5]} for the Dirac equation on Schwarzschild backgrounds. On the other hand, [6]} derived precise asymptotics for general solution on extremal Reissner–Nordström spacetimes. The terms appearing in these asymptotics decay much slower than in the sub-extremal case in view of the horizon instability [7]}, [8]}, [9]}, [10]} and the presence of conserved charges at the event horizon [11]}. An application of the precise asymptotics in the extremal case was presented in [12]} where it was shown that the horizon charges can be computed using only the knowledge of the radiation field at null infinity. On the other hand, proving late-time asymptotics for higher angular frequencies on extremal Reissner–Nordström remains an open problem.
